Question

volume of a cone level 1
score:6/15 penalty: 1 off
question
find the volume of a right circular cone that has a height of 13.8 ft and a base with a radius of 7.8 ft. round your answer to the nearest tenth
of a cubic foot.
answer attempt 1 out of 2
ft³
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Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a right circular cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Substitute the given values into the formula

We are given that \( r = 7.8\) ft and \( h=13.8\) ft. Substituting these values into the formula, we get:
\( V=\frac{1}{3}\times\pi\times(7.8)^{2}\times13.8 \)
First, calculate \( (7.8)^{2}=7.8\times7.8 = 60.84 \)
Then, multiply by \( 13.8 \): \( 60.84\times13.8=60.84\times(10 + 3+0.8)=608.4+182.52 + 48.672=839.592 \)
Now, multiply by \( \frac{1}{3}\pi \): \( V=\frac{1}{3}\times\pi\times839.592=\pi\times279.864 \)
Using \( \pi\approx3.14159 \), we have \( V\approx3.14159\times279.864 \)

Step3: Calculate the numerical value

\( 3.14159\times279.864\approx3.14159\times280 - 3.14159\times0.136\approx879.6452- 0.427\approx879.2182 \)
Rounding to the nearest tenth, we look at the hundredth place. The number is \( 879.2182 \), the hundredth digit is \( 1 \), which is less than \( 5 \), so we round down. So \( V\approx879.2 \)

Answer:

\( 879.2 \)